Summary: Test Two Mathematics 131.01 Spring 2005
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The average was 44.47. The standard deviation was 12.13.
1. Solve
y(3)
(t) - y (t) = et
, y(0) = y (0) = y (0) = 0.
Solution. The characteristic equation is 3
- = 0 the roots of which are -1, 1, 0 so the general
solution of the homogeneous equation is
yh = c1e-t
+ c2et
+ c3.
Since
(D3
- D)tet
= (D + 1)D(D - 1)tet
= (D + 1)Det
= 2et
we see that a particular solution of the original equation is